What is the difference between the area of a square with a two centimeter side length and the area of a square whose sides are four centimeters longer?
We have two squares. One square has a side length of two centimeters. The other square has a side length of four centimeters longer than our first square. This means it’s two centimeters plus four centimeters for the side length or six centimeters.
Our question has asked us what’s the difference between these areas. Before we can take the difference between the areas, we need to find the area of each of these squares. Remember that to find the area of a square, we multiply its side by its side. Written another way, area equals side squared. This means that the area of our small circle equals two squared. And the area of our large square equals six squared. Two squared equals two times two. Two times two equals four. The area of our small square is four centimeters squared. Six squared equals six times six. The area of our larger square equals thirty-six centimeters squared.
Now that we found the areas, we can get back to the problem at hand which was asking us what the difference between the areas are. Thirty-six centimeters squared minus four centimeters squared will tell us what the difference between these two areas is. Thirty-six minus four equals thirty-two. The difference between the area of our larger square and our smaller square equals thirty-two centimeters squared. In problems like these, don’t forget to add the units squared that you’re working with.